$(102)^4=$ ?
$(102)^4=$ ?
- 108242316
- 108423216
- 102843216
- 108243216
Solution
$
\text { } \begin{aligned}
(102)^4= & (100+2)^4 \\
= & { }^4 C_0(100)^4 \cdot 1+{ }^4 C_1(100)^3 \cdot 2^1 \\
& \quad+{ }^4 C_2(100)^2 \cdot 2^2+{ }^4 C_3(100)^1 \cdot 2^3 \\
& \quad+4 C_4(100)^0 2^4 \\
= & (100)^4+4(100)^3 \cdot 2+6(100)^2 \cdot 4 \\
& \quad+4(100) 8+1 \cdot 1 \cdot 16 \\
= & 100000000+8000000+240000 \\
= & 108243216
\end{aligned}
$
Hence, option (4) is correct
Asked in: AP EAMCET 2020 (22 Sep Shift 2)
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